DE102015115150B4 - Method for determining the phase information and counterweights of an imbalance and device for this purpose - Google Patents

Abstract

Method for determining the phase information of an imbalance (U) of a rotating body (11), in which the axis of rotation (YR) does not correspond to the main axis of inertia (YT), characterized by a) determining a reference amplitude of an imbalance (U) of the rotating body (11) induced vibration by means of a sensor (14) stationary with respect to the rotating body (11) in a reference measurement, b) placing an additional mass (MZ, P1) on the body at a predetermined radius to the axis of rotation (YR) a first position and determining a first amplitude (A1) of the imbalance (U) of the rotating body (11) changed by the additional mass (MZ, P1) induced vibration by means of the sensor (14) in a first measurement, c) changing the position the additional mass (MZ, P1) so that the additional mass (MZ, P1) on the body while maintaining the specified radius at a second position different from the first position under a defined change ngswinkel is arranged in relation to the first position, and determining a second amplitude (A2) of the imbalance of the rotating body (11) changed by the additional mass (MZ, P2) induced vibration by means of the sensor in at least one second measurement, and with the Steps that can be carried out by a microprocessor-controlled arithmetic unit: d) Calculate, by means of a microprocessor-controlled arithmetic unit (16), phase information of the unbalance (U) as a function of the measured amplitudes, in which the amplitudes in relation to a Cartesian coordinate system each form a circle with a radius that corresponds in terms of magnitude to the respective amplitude, around a common center point, which represents the origin of the Cartesian coordinate system, and the intersection of the circle of the reference amplitude with a reference axis running through the origin of the Cartesian coordinate system forms the center of an additional circle, which is both the circle of the first Amplitude (A1) as well as the circle of the second amplitude (A2) intersects at least one intersection point, Point of intersection (P1) of the first amplitude (A1) and a second leg through the point of intersection (P2) of the second amplitude (A2), corresponds to the defined change angle of the second measurement, corresponds to and in which a first leg runs through the intersection (P1, P2) of the first or second amplitude (A1, A2) and a second leg represents the reference axis, is calculated, and • where the phase information of the unbalance (U) as a function of the calculated system rotation angle (a) and that position at which the additional mass was arranged on the body and that of the first leg of the Sy star rotation angle (α) corresponds to the underlying amplitude, is calculated.

Description

The invention relates to a method for determining the phase information of an imbalance in a rotating body in which the axis of rotation does not correspond to the main axis of inertia. The invention also relates to a device for this purpose.

The invention also relates to a method for determining counterweights to compensate for an imbalance in a rotating body in which the axis of rotation does not correspond to the main axis of inertia. The invention also relates to a device for this purpose.

In the case of rotating bodies, in particular in the case of rotationally symmetrical bodies such as a wheel, it is desirable that the rotating body is free from parasitic forces that lead to out-of-round running. Such forces arise when the axis of rotation of the rotating body does not correspond to the main axis of inertia of the body (in relation to a plane), so that there is an imbalance in the distribution of forces during rotation, which then results in vibration.

If the axis of rotation does not correspond to the main axis of inertia, one also speaks of an imbalance, in which the rotating body has a centrifugal force behavior internalized around the entire circumference of rotation, which results in a vibration induced by the imbalance (depending on the rotation speed) and with the help of sensors (acceleration sensors , Force sensors, deformation sensors) can be measured.

However, in order to precisely localize an imbalance and, if necessary, to compensate for the imbalance by arranging counterweights or counterweights, it is necessary to determine the position or phase information of the imbalance in addition to determining the amplitude. Because only with the help of the position of the imbalance can the counterweight be attached to the opposite position, for example, whereby the imbalance is compensated by shifting the axis of inertia onto the axis of rotation.

The position of the imbalance or phase information of the imbalance is the direction in which the main axis of inertia deviates from the axis of rotation.

In order to determine the phase information or position of the imbalance, ie the direction of the imbalance, it is usually necessary that the device that sets the body in rotation and measures the amplitude of the vibration also determines the phase information, which the entire device clearly determines more complicated and more expensive to buy. If it is not possible due to the design of the device to determine the phase or phase information of the imbalance, it is not possible using current methods to determine the position of the imbalance in relation to the rotating body.

From the CN 1269504 A a method for determining an imbalance is known in which only three measurements are carried out. In addition, a reference measurement is carried out once and then two measurements with an additional weight, the additional weight being arranged at an angle of 90 ° with respect to the first measurement in the second measurement. The reference amplitude is arranged as a circle with a center at the origin of a Cartesian coordinate system, the circle of the reference amplitude intersecting the x-axis and the y-axis at predetermined points. The first measurement is also understood as a circle, the center of which is the intersection of the reference amplitude with the x-axis. The procedure for the second amplitude is analogous to this. A vector is then placed from the origin of the Cartesian coordinate system to the point of intersection of the two measurement amplitudes, so that the direction of the imbalance is displayed.

From the US 2007/0186651 A1 a method and apparatus for determining hidden spoke arrangements for balancing the weight of a wheel is known.

It is therefore the object of the present invention to provide a device and a method with which the determination of phase information of an imbalance of a rotating body is also possible without direct phase measurement or rotation angle measurement. It is also an object of the present invention to specify a method and a device with which it is possible to determine counterweights to compensate for the existing imbalance without directly measuring the phase information of the imbalance.

The first aspect of the object is achieved with the method for determining the phase information of an imbalance according to claim 1 and a device for determining the phase information according to claim 8.

Accordingly, a method is proposed for determining the phase information of an imbalance in a rotating body, in which the axis of rotation does not correspond to the main axis of inertia, in which the phase does not need to be detected during the measurement itself. Measurements only have to be made with regard to the amplitude of the imbalance in order to then determine the phase information using the method according to the invention.

For this purpose, a so-called reference measurement is first carried out, in which a reference amplitude of the imbalance of a vibration induced by the imbalance of the rotating body is determined by means of a sensor which is fixed in relation to the rotating body. The reference amplitude can be, for example, the maximum amplitude of the vibration, an existing mass unbalance mainly being expressed in the amplitude of the rotational frequency.

This reference amplitude can be measured, for example, with the aid of acceleration sensors or force sensors or, if necessary, with the aid of deformation sensors. For example, it is conceivable that the amplitude is determined from the vibration at the position of the sensor, for example with the aid of a smartphone.

After the reference measurement has been carried out and the reference amplitude has been determined, an additional mass is arranged on the rotating body at a predetermined radius to the axis of rotation at a first position, preferably without changing the sensor position, and a further amplitude measurement is carried out by placing the body back in Rotation is offset (preferably with a constant rotation speed as for the reference measurement) and a first amplitude with respect to the imbalance is determined from the vibration induced by the imbalance. This can also be the maximum amplitude, for example.

By attaching an additional mass below a predetermined radius, the main axis of inertia is changed in relation to the axis of rotation, whereby an amplitude different from the reference measurement can be recorded as a system response at the same sensor position. This is because, depending on the deviation of the additional mass from the direction of the imbalance, the system response is noticeable through an increase in the amplitude of the reference amplitude or through a reduction in the amplitude compared to the reference amplitude. Without recognizing phase information, however, it is not possible to determine the phase information of the actual imbalance from this data alone.

A second measurement is therefore carried out in the next step, the position of the additional mass on the body being shifted beforehand while maintaining the predetermined radius at a second position different from the first position at a defined angle of change. In other words, with respect to the axis of rotation, the additional mass is arranged from the first position at a predefined angle, for example 90 degrees, at a second position with the same radius with respect to the first position, so that the additional mass is phase-shifted depending on the specified change angle while the radius remains the same . The body is then set in rotation again (preferably at a constant rotational speed), with the aid of the sensor at the preferably unchanged sensor position, a second amplitude being recorded in a second measurement. This can also be the maximum amplitude, for example.

As a result, there are now three amplitude values, namely on the one hand the amplitude value of the reference amplitude of the reference measurement, in which an amplitude of the unbalance was determined without any additional masses, and two further additional measurements, in each of which an additional mass on the rotating body with a constant radius and a given angle arranged and the corresponding amplitude of the resulting imbalance is measured. The additional mass in the two measurements is identical, as is the speed of rotation and the position of the sensor in the non-rotating system.

The phase information of the imbalance can now be determined analytically from these three values and the specified change angle.

In this calculation, the amplitudes in relation to a Cartesian coordinate system each form a circle with a radius that corresponds to the magnitude of the respective measured amplitude, around one common center point that represents the origin of the Cartesian coordinate system. All amplitude circles would intersect a reference axis (ray or half-line with the origin in the origin of the Cartesian coordinate system) running through the origin of the Cartesian coordinate system, the point of intersection of the amplitude circle of the reference amplitude with this reference axis forming the center of an additional circle, which forms both the amplitude circle of the first Amplitude as well as the amplitude circle of the second amplitude intersects in each case at least one point of intersection.

The radius of this additional circle is calculated in such a way that an angle whose vertex corresponds to the center point of the additional circle and at which a first leg runs through the intersection with the first amplitude circle and a second leg through the intersection of the second amplitude circle, the defined change angle of the second Measurement corresponds.

The radius corresponds to an additional amplitude resulting from the additional masses, which are arranged somewhere on this circle around the origin of the original imbalance. However, since the additional masses were shifted between the first and the second measurement at a given angle of change, this must also be reflected in the intersection points of the additional circle. Accordingly, the radius of the additional circle is calculated so that the condition is met that an angle whose vertex corresponds to the center point of the additional circle at which a first leg through the intersection of the first amplitude circle or the first amplitude and a second leg through the intersection of the second amplitude circle or the second amplitude, corresponds to the defined angle of change of the second measurement. If such a radius has been calculated, it corresponds to the additional amplitude that results from the arrangement of the additional masses when there is an imbalance.

Based on this, a system rotation angle is then calculated, which describes the phase shift of the position of the respective additional mass in the respective measurement from the actual original unbalance by calculating the angle whose apex corresponds to the center point of the additional circle and at which a first leg passes through the intersection of the first or second amplitude circle and a second leg represents the reference axis. In other words, that angle in the geometric construction is determined which spans between the reference axis as a leg on the one hand and the point of intersection with one of the amplitude circles as a second leg on the other hand. This angle indicates by how many degrees the position for the additional mass of the respective amplitude is away from the actual imbalance.

Based on this, the phase information of the imbalance can then be calculated as a function of the calculated system rotation angle and that position at which the additional mass was arranged on the body and which corresponds to the amplitude on which the first leg of the system rotation angle is based.

Based on this, the phase information can be calculated very specifically, so that the unbalance can be calculated analytically exactly with only three measurements without a phase measurement during the amplitude determination.

Advantageously, based on this phase information, a counter-mass can then be calculated, which is arranged at the opposite position of the calculated phase information of the unbalance on the body in order to compensate for the unbalance, the counter-mass being calculated as a function of the previously determined reference amplitude.

However, it is also conceivable that, based on the two positions at which the additional mass is arranged, two counter-masses in this regard are calculated in order to compensate for the imbalance. For this purpose, a countermass with respect to the position of the additional mass depending on the defined change angle, the calculated system rotation angle, a first amplitude vector that corresponds to the distance between the center of the additional circle and the intersection of the first amplitude circle and a second amplitude vector that corresponds to the distance between the center of the Additional circle and the intersection of the second amplitude circle corresponds, calculated to compensate for the existing imbalance when the respective counterweights at the position of the additional mass, or when the absolute value is negative, are arranged opposite one another.

The reference axis is advantageously formed by the abscissa axis or the ordinate axis of the Cartesian coordinate system and thus simplifies the calculation.

Furthermore, it is advantageous if the defined change angle is 90 degrees or an integral multiple thereof, which simplifies the calculation.

Incidentally, the object is also achieved with patent claim 4 with regard to a method for determining counterweights to compensate for an imbalance in a rotating body, the method steps up to the determination of the system rotation angle being identical to patent claim 1. In this respect, the common inventive concept here is that from three measurements without phase information, at least the system angle of rotation from which one position of the additional mass deviates from the unbalance can be determined. To compensate for the imbalance, however, it is proposed that the respective counter mass for the position and the additional masses be calculated as a function of the defined change angle, the calculated system rotation angle, a first amplitude vector and a second amplitude vector in order to compensate for the existing imbalance. Based on the vector calculation, the counterweights are determined in such a way that they point vectorially in the direction of the origin of the Cartesian coordinate system in relation to the intersection points defined in the Cartesian coordinate system and can thus compensate for the imbalance.

The first amplitude vector describes the distance between the center of the additional circle and the point of intersection of the first amplitude or the first amplitude circle, while the second amplitude vector describes the distance between the center of the additional circle and the point of intersection of the second amplitude circle.

This makes it possible, without precise knowledge of the actual imbalance, to calculate a counter-mass for the positions on which the additional mass was arranged, whereby when the counter-masses are arranged at the positions of the additional masses or at the opposite position, if the calculated counter-mass should be negative, the imbalance can then be compensated.

• 1 - Schematische Darstellung einer erfindungsgemäßen Vorrichtung;
• 2 - Schematische Darstellung der drei Messreihen;
• 3 - Geometrische Darstellung des Berechnungsverfahrens Zur Phaseninformationsermittlung;
• 4 - Geometrische Darstellung der Berechnung zur Bestimmung der Gegenmassen.

The invention is explained by way of example with reference to the accompanying figures. Show it:

• 1 - Schematic representation of a device according to the invention;
• 2 - Schematic representation of the three series of measurements;
• 3 - Geometric representation of the calculation method for determining phase information;
• 4th - Geometric representation of the calculation to determine the counterweights.

1 shows schematically the device 10 with which the imbalance U of a spinning body 11 can be determined, the imbalance U of the rotating body 11 is determined by a deviation in the axis of rotation Y _R from the main axis of inertia Y _T .

The solid of revolution 11 becomes with its axis of rotation Y _R on a rotor axis 12th the device 10 plugged in and locked in place. The rotor axis 12th stands with an engine 13th in a force-acting connection, so by rotating the rotor axis 12th the body 11 to put in a rotary motion.

At the device 10 is a sensor 14th provided as a force or acceleration sensor vibrations of the housing 15th the device 10 can determine. Since the unbalance in the plane of rotation (static unbalance) is to be determined here, the sensor is 14th also set up a corresponding vibration within the plane of rotation of the body 11 to determine. The one due to the imbalance U of the rotating body 11 The vibration caused is due to the suspension of the rotor axis 12th on the housing 15th and the fixed connection of the motor to the housing 15th transferred to this so that the sensor 14th can determine this vibration and thus the amplitudes, for example in the form of a maximum amplitude.

This is what the sensor stands for 14th with one arithmetic unit 16 signaling in connection, which also includes the engine 13th can drive. However, this is not absolutely necessary. The arithmetic unit 16 is set up in such a way that it carries out the corresponding information, such as the phase information or the calculation of the counter mass according to the present invention, based on the three measurements to be carried out, as will be shown later.

2 shows the sequence of measurements to determine the required amplitudes. The rotating body 11 shows an imbalance due to the deviations from the axis of rotation Y _R from the main axis of inertia Y _T .

In step a) the rotatable body is 11 set in a rotational movement without any additional masses being arranged on the body for this purpose. As a result, the sensor of the device supplies a reference amplitude signal which, for example, corresponds to the maximum amplitude of a measured vibration.

An additional mass is required for a second measurement M _{z, P1} at a first position on the rotatable body 11 arranged, namely under a predetermined radius r _M. The vibration measurement is then carried out again at the same speed, the first amplitude again being determined from a measured vibration as the maximum amplitude from the vibration.

Then in step c) the position of the additional mass is adjusted by an angle φ offset, but while maintaining the radius r _M , so that the additional mass is now in a second position on the rotatable body 11 is arranged. This additional mass in step c) is as M _{Z, P2} referred to, the additional mass itself remains the same, but the position according to the angle φ changed.

Another measurement is carried out at the same speed, a second amplitude being determined from the measured vibration as the maximum amplitude in this measurement.

3 shows the geometric calculation basis for calculating the phase information.

First, a Cartesian coordinate system X, Y is defined, in which the origin of the Cartesian coordinate system denotes the case in which the main axis of inertia and the axis of rotation are identical, so that there is no imbalance. However, since no phase information is contained based on the measurements, starting from the origin of the Cartesian coordinate system, the measured amplitudes describe a circle around the origin. The first measurement to determine the first amplitude with the additional mass at the first position is called A ₁ denotes, while the second measurement with the additional mass at the second position has a second amplitude A ₂ brings forth.

The reference amplitude, i.e. the reference measurement without any additional masses, would also define a circle around the origin of the Cartesian coordinate system. However, this is not shown for reasons of clarity, since this is not necessary for the further calculation.

Rather, it became the reference amplitude U plotted as an unbalance on the abscissa axis (X) of the Cartesian coordinate system, which is an equivalent of the intersection of the reference amplitude with the reference axis.

The point U forms the center of a circle, the radius of which represents the additional amplitude that is caused by the two measurements with the additional mass. Since no phase information is available here either, these additional amplitudes lie on a circle around the origin U around, with only the angle of change with which the additional mass is arranged at an angle on the rotating body as φ is known. That angle φ must therefore also find himself in the circle.

In the embodiment of 3 the angle is different from 90 ° or an integer multiple of 90 °, so that the angle here φ still has a so-called Δ _Ψ with which the 90 ° deviation is defined.

Since this is also part of the invention, the complete calculation method is shown here. However, it becomes an angle of change φ taken, which has 90 ° or an integral multiple thereof, the calculation is simplified in some places.

The radius Z this additional circle corresponds to the additional amplitude due to the additional masses. However, Z is initially unknown, so that a radius must be calculated for the additional circle in which the condition is met that on the one hand the additional circle intersects the amplitude circles in at least one intersection point and on the other hand that the intersection points P ₁ and P ₂ are such that they are together with the center point U of the additional circle the angle φ stretch.

In other words, between the midpoint U and the intersections P ₁ with the first amplitude circle of the amplitude A ₁ a first leg is defined and with the center U and the intersection P ₂ of the second amplitude circle of the second amplitude P ₂ a second leg is defined, where between the first leg ( U , P ₁ ) and the second leg ( U , P ₂ ) the angle φ is spanned, which corresponds to the angle of change of the additional masses between the two first and second measurements.

If such an additional circle is found with a radius equal to Z, then the first leg in the training example defines the 1 , ie the leg between the center of the additional circle U and the intersection P ₁ of the amplitude circle of the first amplitude A ₁ and the reference axis an angle α, which is in relation to the position of the additional mass in the first measurement, which is the first amplitude A ₁ and thus the intersection P ₁ corresponds to the deviation of this position of the additional mass of the first measurement from the direction of the unbalance and thus contains the phase information.

Based on the known positions of the additional mass of the first measurement and the calculated angle α the position of the imbalance and thus the phase information of the imbalance can thus be determined by dividing the position of the additional mass of the first measurement through the angle α is corrected.

As an alternative to this, of course, the second leg, which is the route between the center point U of the additional circle and the intersection P ₂ of the second amplitude circle of the second amplitude A ₁ is defined, can be used to calculate an angle with the reference axis, in which case, of course, the position of the additional mass of the first measurement does not have to be used, but rather the position of the additional mass in the second measurement, which changes by a certain angle φ from the first position. This is of course a mathematical equivalent.

Once the phase information and thus the direction of the unbalance has been found, a counterweight or a counterweight can be arranged at the opposite position based on the measured reference amplitude, whereby the unbalance is compensated and the main axis of inertia then corresponds to the axis of rotation.

On the basis of the following calculations, which are given as examples, the geometrical relationship shown above can be calculated analytically, which results in a clear solution.

mit $$P_{1x}=Z\cdot cos\left(\alpha \right)+U$$

und $$P_{1y}=Z\cdot sin\left(\alpha \right)$$

(2) und (3) eingesetzt in (1) und umgeformt ergibt: $$A_1{}^2=U^2+Z^2+2UZ\cdot cos\left(\alpha \right),$$

und damit $$\text{cos}\left(\alpha \right)=\frac{A_1^2{U}^2-Z^2}{2UZ}$$

First amplitude of measurement 1 including additional mass: $${\mathrm{A.}}_1=\sqrt{P_{1x}^2+P_{1y}^2,}$$

With $$P_{1x}=Z\cdot cOs\left(\alpha \right)+U$$

and $$P_{1y}=Z\cdot sin\left(\alpha \right)$$

(2) and (3) inserted in (1) and transformed results in: $${\mathrm{A.}}_1{}^2=U^2+Z^2+2UZ\cdot cOs\left(\alpha \right),$$

and thus $$\text{cos}\left(\alpha \right)=\frac{{\mathrm{A.}}_1^2{U}^2-{\mathrm{<figure-callout\; id="2"\; label="Z"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">Z</figure-callout>}}^2}{2UZ}$$

$$P_{2x}=U-Z\cdot sin\left(\alpha +\mathrm{\Delta \psi }\right)\text{ und}$$

$$P_{2y}=Z\cdot cos\left(\alpha +\mathrm{\Delta \psi }\right)$$

The second amplitude of measurement 2 including additional mass is: $${\mathrm{A.}}_2=\sqrt{P_{2x}^2+P_{2\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">y</figure-callout>}}^2},\text{With}$$

$$P_{2x}=U-Z\cdot sin\left(\alpha +\mathrm{\Delta \psi }\right)\text{and}$$

$$P_{2y}=Z\cdot cOs\left(\alpha +\mathrm{\Delta \psi }\right)$$

und $$K_2=sin\left(\mathrm{\Delta \psi }\right)$$

kan folgender Zusammenhang ermittelt werden: $$sin\left(\alpha \right)=\frac{U^2+Z^2-A_2^2-K_2\left(A_1^2-Z^2-U^2\right)}{2U2K_1}$$

After reshaping and substituting: $$K_1=cOs\left(\mathrm{\Delta \psi }\right)$$

and $${\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">K</figure-callout>}}_2=sin\left(\mathrm{\Delta \psi }\right)$$

the following relationship can be determined: $$sin\left(\alpha \right)=\frac{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">U</figure-callout>}}^2+Z^2-{\mathrm{A.}}_2^2-K_2\left({\mathrm{A.}}_1^2-Z^2-U^2\right)}{2U2K_1}$$

erhält man mit (5) und (11) den Drehwinkel: $$\alpha =\text{arctan}\left(\frac{U^2+Z^2-A_2^2-K_2\left(A_1^2-Z^2-U^2\right)}{K_1\left(A_1^2-Z^2-U^2\right)}\right)$$

If you set now $$tan\left(\alpha \right)=\frac{sin\left(\alpha \right)}{cOs\left(\alpha \right)}$$

the angle of rotation is obtained with (5) and (11): $$\alpha =\text{arctan}\left(\frac{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">U</figure-callout>}}^2+Z^2-{\mathrm{A.}}_2^2-K_2\left({\mathrm{A.}}_1^2-Z^2-U^2\right)}{K_1\left({\mathrm{A.}}_1^2-Z^2-U^2\right)}\right)$$

Here are still α and Z unknown. An analytical solution can be found using the following relationship. $$si{n}^2\alpha +cO{s}^2\alpha =1$$

for Z By inserting and reshaping (5) and (11), 4 solutions for Z can be determined. solve $$\begin{array}{l}\left(\frac{{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">U</figure-callout>}}^2+Z^2-{\mathrm{A.}}_2^2-K_2\left({\mathrm{A.}}_1^2-Z^2-U^2\right)}{\sqrt{1-{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">K</figure-callout>}}_2^2}}\right)+\hfill \\ {\left({\mathrm{A.}}_1^2-U^2-Z^2\right)}^2-\mathrm{4th}{U}^2{\mathrm{<figure-callout\; id="2"\; label="Z"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">Z</figure-callout>}}^2=0\hfill \end{array}$$

for Z

$$\begin{array}{l}Z=\pm \frac{1}{\sqrt{2}}\hfill \\ (\surd (1/\left(K_2+1\right)(-\surd (\left(K_2^2-1\right)(-4A_1^2{K}_2{U}^2--4A_2^2{K}_2{U}^2-4A_1^2{U}^2-4A_2^2{U}^2+A_1^4+\hfill \\ A_2^4-2A_1^2{A}_2^2+4K_2^2{U}^4+8K_2{U}^4))+A_1^2{K}_2+A_2^2{K}_2+\hfill \\ A_1^2+A_2^2-2K_2^2{U}^2-2K_2{U}^2)))\text{ and }{K}_2+1\ne 0\text{ and }{K}_2-1\ne 0\hfill \end{array}$$

Results: $$\begin{array}{l}Z=\pm \frac{1}{\sqrt{2}}\\ \begin{array}{l}\hfill \\ (\surd (1/\left({\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">K</figure-callout>}}_2+1\right)(-\surd (\left({\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">K</figure-callout>}}_2^2-1\right)(-\mathrm{4th}{\mathrm{A.}}_1^2{K}_2{U}^2--\mathrm{4th}{\mathrm{A.}}_2^2{K}_2{U}^2-\mathrm{4th}{\mathrm{A.}}_1^2{U}^2-\mathrm{4th}{\mathrm{A.}}_2^2{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">U</figure-callout>}}^2+{\mathrm{A.}}_1^{\mathrm{4th}}+\hfill \\ {\mathrm{A.}}_2^{\mathrm{4th}}-2{\mathrm{A.}}_1^2{\mathrm{A.}}_2^2+\mathrm{<figure-callout\; id="2"\; label="4th\; K"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">4th</figure-callout>}{K}_{}^{}{}_2^2{U}^{\mathrm{4th}}+\mathrm{8th}{K}_2{U}^{\mathrm{4th}}))+{\mathrm{A.}}_1^2{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">K</figure-callout>}}_2+{\mathrm{A.}}_2^2{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">K</figure-callout>}}_2+\hfill \\ {\mathrm{A.}}_1^2+{\mathrm{A.}}_2^2-2{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">K</figure-callout>}}_2^2{U}^2-2K_2{U}^2)))\text{<figure-callout id="2" label="other K" filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png" state="{{state}}">other</figure-callout>}{K}_{}{}_2+1\ne 0\text{other}{K}_2-1\ne 0\hfill \end{array}\end{array}$$

$$\begin{array}{l}Z=\pm \frac{1}{\sqrt{2}}\hfill \\ (\surd (1/\left({\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">K</figure-callout>}}_2+1\right)(-\surd (\left({\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">K</figure-callout>}}_2^2-1\right)(-\mathrm{4th}{\mathrm{A.}}_1^2{K}_2{U}^2--\mathrm{4th}{\mathrm{A.}}_2^2{K}_2{U}^2-\mathrm{4th}{\mathrm{A.}}_1^2{U}^2-\mathrm{4th}{\mathrm{A.}}_2^2{\mathrm{<figure-callout\; id="2"\; label="U"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">U</figure-callout>}}^2+{\mathrm{A.}}_1^{\mathrm{4th}}+\hfill \\ {\mathrm{A.}}_2^{\mathrm{4th}}-2{\mathrm{A.}}_1^2{\mathrm{A.}}_2^2+\mathrm{<figure-callout\; id="2"\; label="4th\; K"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">4th</figure-callout>}{K}_{}^{}{}_2^2{U}^{\mathrm{4th}}+\mathrm{8th}{K}_2{U}^{\mathrm{4th}}))+{\mathrm{A.}}_1^2{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">K</figure-callout>}}_2+{\mathrm{A.}}_2^2{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">K</figure-callout>}}_2+\hfill \\ {\mathrm{A.}}_1^2+{\mathrm{A.}}_2^2-2{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">K</figure-callout>}}_2^2{U}^2-2K_2{U}^2)))\text{<figure-callout id="2" label="other K" filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png" state="{{state}}">other</figure-callout>}{K}_{}{}_2+1\ne 0\text{other}{K}_2-1\ne 0\hfill \end{array}$$

With the help of equations (13) and (15) it can be shown that a plausible solution for Z and α can be calculated from only 3 measured amplitudes.

After the values for Z and α are known, the appropriate masses can be used to remove the imbalance U be calculated. Starting from the point U In order to eliminate the imbalance, it is necessary to determine a suitable counter mass in the direction of the vector Vu. This can be done, for example, with a corresponding mass in the direction of Vu, or the components of the azimuth points used to determine the unbalance are broken down and used. To calculate the required masses, a factor F is determined in each case, which represents the necessary amount for the directions V ₁ and V ₂ .

$$\overrightarrow{m_2}=F_2\cdot \overrightarrow{v_2}=F_2\cdot \left(\begin{array}{c}{P}_{2x}-U\\ P_{2y}\end{array}\right)$$

$$\overrightarrow{v_U}=\left(\begin{array}{c}-U\\ 0\end{array}\right)=\overrightarrow{m_1}+\overrightarrow{m_2}$$

The following relationships can be seen in the derivation sketch: $$\overrightarrow{m_1}={\mathrm{F.}}_1\cdot \overrightarrow{v_1}={\mathrm{F.}}_1\cdot \left(\begin{array}{c}{P}_{1x}-U\\ P_{1y}\end{array}\right)$$

$$\overrightarrow{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">m</figure-callout>}}_2}={\mathrm{F.}}_2\cdot \overrightarrow{{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">v</figure-callout>}}_2}={\mathrm{F.}}_2\cdot \left(\begin{array}{c}{P}_{2x}-U\\ P_{2y}\end{array}\right)$$

$$\overrightarrow{v_U}=\left(\begin{array}{c}-U\\ 0\end{array}\right)=\overrightarrow{m_1}+\overrightarrow{{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="DE102015115150B4\_0027.png,DE102015115150B4\_0028.png"\; state="\{\{state\}\}">m</figure-callout>}}_2}$$

The y-component can be transformed into: $${\mathrm{F.}}_2=-{\mathrm{F.}}_1\frac{P_{1y}}{P_{2y}}$$

From (19) with (17) and (18) it follows from the x-component: $${\mathrm{F.}}_1=\frac{U}{\left(U-P_{1x}+\frac{P_{1y}}{P_{1y}}\left(P_{2x}-U\right)\right)}$$

$$M_2=F_2\cdot M$$

The two factors are thus known and the final masses M ₁ and M ₂ for eliminating the imbalance can be determined. The amplitude factors are converted into corresponding masses with the applied test mass M. Using equations (16) and (17), the masses M ₁ and M ₂ can be calculated as: $${\mathrm{M.}}_1={\mathrm{F.}}_1\cdot \mathrm{M.}$$

$${\mathrm{M.}}_2={\mathrm{F.}}_2\cdot \mathrm{M.}$$

If there is a positive sign, the calculated mass is mounted at the azimuth position of the test mass, in the case of a negative sign exactly opposite (180 °), or if possible the corresponding mass is removed from the azimuth position of the test mass.

List of reference symbols

10

contraption

11

rotating body

12th

Rotor axis

13th

engine

14th

sensor

15th

casing

16

Arithmetic unit

U

Imbalance

Y _R

Axis of rotation

Y _T

Main axis of inertia

M _{Z, P1}

Additional mass at position 1

M _{Z, P2}

Additional mass at position 2

A ₁

first amplitude in the first measurement

A ₂

second amplitude in the second measurement

P ₁

Point of intersection of the amplitude circle of the first amplitude with the additional circle

P ₂

Point of intersection of the amplitude circle of the second amplitude with the additional circle

α

System rotation angle

Z

Additional amplitude, radius of the additional circle

φ

Change angle of the position of the additional mass between the first and second measurement

Claims (9)

Method for determining the phase information of an imbalance (U) of a rotating body (11), in which the axis of rotation (Y _R ) does not correspond to the main axis of inertia (Y _T ), characterized by a) determining a reference amplitude of a due to the imbalance (U) of the rotating body (11) induced vibration by means of a sensor (14) fixed in relation to the rotating body (11) in a reference measurement, b) arranging an additional mass (M _{Z, P1} ) on the body at a predetermined radius to the axis of rotation (Y _R ) at a first position and determining a first amplitude (A ₁ ) of the imbalance (U) of the rotating body changed by the additional mass (M _{Z, P1)} (11) induced vibration by means of the sensor (14) in a first measurement, c) changing the position of the additional mass (M _{Z, P1} ) so that the additional mass (M _{Z, P1} ) on the body while maintaining the specified radius on a from the first position different second position is arranged at a defined angle of change with respect to the first position, and determining a second amplitude (A ₂ ) of the imbalance of the rotating body (11) changed by the additional mass (M _{Z, P2) induced vibration} by means of the sensor in at least one second measurement, and with the steps that can be carried out by a microprocessor-controlled arithmetic unit: d) Calculating, by means of a microprocessor-controlled arithmetic unit (16), phase information of the imbalance (U) as a function of the measured amplitudes by referring to the amplitudes on a Cartesian coordinate system in each case a circle with a radius that corresponds to the magnitude of the respective amplitude en common center point, which represents the origin of the Cartesian coordinate system, and the intersection of the circle of the reference amplitude with a reference axis running through the origin of the Cartesian coordinate system forms the center of an additional circle, which includes both the circle of the first amplitude (A ₁ ) and the Circle of the second amplitude (A ₂ ) intersects at least one point of intersection, the radius of the additional circle is calculated in such a way that an angle whose apex corresponds to the center point of the additional circle and at which a first leg passes through the point of intersection (P ₁ ) first amplitude (A ₁ ) and a second leg through the intersection (P ₂ ) of the second amplitude (A ₂ ), corresponds to the defined angle of change of the second measurement, • where a system rotation angle (a) whose apex corresponds to the center of the additional circle and in which a first leg through the intersection (P ₁ , P ₂ ) of the e rsten or second amplitude (A ₁ , A ₂ ) and a second leg represents the reference axis, is calculated, and the phase information of the unbalance (U) depending on the calculated system rotation angle (a) and the position at which the additional mass was arranged on the body and which corresponds to the amplitude on which the first leg of the system rotation angle (α) is based, is calculated. Procedure according to Claim 1 , characterized in that the arithmetic unit (16) is set up to calculate a counter mass as a function of the reference amplitude in order to compensate for the existing imbalance (U) when the counter mass is arranged on the body at the opposite position of the calculated phase information of the imbalance (U) becomes. Procedure according to Claim 1 , characterized in that the computing unit (16) is set up, in each case a counter mass with respect to the positions of the additional mass as a function of the defined change angle, the calculated system rotation angle (α), a first amplitude vector that represents the distance between the center of the additional circle and the point of intersection ( P ₁ ) corresponds to the first amplitude (A ₁ ), and to calculate a second amplitude vector, which corresponds to the distance between the center of the additional circle and the intersection (P ₂ ) of the second amplitude (A ₂ ), in order to calculate the existing imbalance (U) to compensate, if the respective counterweight at the position of the additional weight, or if its absolute value is negative, opposite, is arranged. Method for determining counterweights to compensate for an imbalance (U) of a rotating body (11), in which the axis of rotation (Y _R ) does not correspond to the main axis of inertia (Y _T ), characterized by a) determining a reference amplitude of an imbalance caused by (U ) the rotating body (11) induced vibration by means of a sensor stationary with respect to the rotating body (11) in a reference measurement, b) arranging an additional mass (M _{Z, P1} ) on the body at a predetermined radius to the axis of rotation ( Y _R ) at a first position and determining a first amplitude (A ₁ ) of the imbalance of the rotating body (11), which has been changed by the additional mass (M _{Z, P1} ), induced vibration by means of the sensor (14) in a first measurement, c) Changing the position of the additional mass in such a way that the additional mass (M _{Z, P2} ) is defined on the body while maintaining the predetermined radius at a second position different from the first position n change angle is arranged in relation to the first position, and determining a second amplitude (A ₂ ) of the imbalance of the rotating body (11) changed by the additional mass (M _{Z, P2} ) induced vibration by means of the sensor (14) in at least one second measurement, and with the steps that can be carried out by a microprocessor-controlled arithmetic unit: d) calculating, by means of a microprocessor-controlled arithmetic unit (16), in each case a counterweight with respect to the positions of the additional masses, in that the amplitudes in relation to a Cartesian coordinate system are each a circle with a radius, which corresponds to the magnitude of the respective amplitude, around a common center, which represents the origin of the Cartesian coordinate system, and the intersection of the circle of the reference amplitude with a reference axis running through the origin of the Cartesian coordinate system forms the center of an additional circle, which is both the circle of the first A. mplitude (A ₁ ) as well as the circle of the second amplitude (A ₂ ) intersects at least one point of intersection, the radius of the additional circle is calculated in such a way that an angle whose apex corresponds to the center of the additional circle and at which a first leg through the intersection (P ₁ ) of the first Amplitude (A ₁ ) and a second leg through the intersection (P ₂ ) of the second amplitude (A ₂ ), corresponds to the defined change angle of the second measurement, • where a system rotation angle (a) whose apex corresponds to the center point of the additional circle and at which a first leg runs through the intersection (P ₁ , P ₂ ) of the first or second amplitude (A ₁ , A ₂ ) and a second leg represents the reference axis, is calculated, and depending on the defined change angle, the calculated System rotation angle (a), a first amplitude vector which corresponds to the distance between the center of the additional circle and the point of intersection (P ₁ ) of the first amplitude (A ₁ ), and a second amplitude vector which corresponds to the distance between the center of the additional circle and the point of intersection (P ₂ ) corresponds to the second amplitude (A ₂ ), the respective counter mass is calculated for the position of the additional mass in order to compensate for the existing imbalance (U) ichen if the respective counter-mass is arranged at the position of the additional mass or, if its absolute value is negative, opposite. Method according to one of the preceding claims, characterized in that the reference axis is formed by the abscissa axis or the ordinate axis of the Cartesian coordinate system. Method according to one of the preceding claims, characterized in that the defined change angle is 90 ° or an integral multiple thereof. Method according to one of the preceding claims, characterized in that, in addition to the reference measurement, only the first measurement and the second measurement are carried out. Device for determining the phase information of an imbalance (U) of a rotating body (11), in which the axis of rotation (Y _R ) does not correspond to the main axis of inertia (Yτ), with a rotation device which is designed to rotate the body received in the rotation device, and with a sensor (14) for determining an amplitude of a vibration induced by the unbalance (U) of the rotating body (11), characterized in that the device has a computing unit (16) which is set up to process the phase information of the unbalance ( u) according to one of the Claims 1 to 3 and 5 to 7th to determine. Device for determining counterweights to compensate for an imbalance (U) of a rotating body (11), in which the axis of rotation (Y _R ) does not correspond to the main axis of inertia (Y _T ), with a rotation device that is used to rotate the body received in the rotation device is formed, and with a sensor (14) for determining an amplitude of a vibration induced by the unbalance (U) of the rotating body (11), characterized in that the device has a computing unit (16) which is set up, the counterweight to compensate for the imbalance (U) according to one of the Claims 4 to 7th to determine.

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